To be clear, the rights (thinking primarily of copyright here) of the answers on this sub remain with the author of the answer. These answers are not public domain and cannot be reused without proper authorisation (from the respective authors). Anyone wanting to publish a book would face the difficult task of getting authorisation for all the answers they'd want to include.

The biggest issue would be money. Not raising printing costs, but what happens to the money gained from book sales? It would be a nightmare to divide among contributors. There's not that much that we can use money for to benefit the whole of AH, especially since this probably won't be a steady income. I would support profits going to a charity, or some central endeavor that everyone can benefit from.

A collection of questions and answers seems likely to be just a sprawl of information (and opinion) about topics scattered across time and space (but weirdly concentrated on a few areas and topics).

A more interesting book might be some sort of thoughtful analysis of the questions and answers in the sub, with reflection on what this indicates about the emotional connection between the reddit audience of today and the events of the past? What causes questions or answers to be popular and upvoted? What leads to long multi-answer discussions, vs what is ignored? What seem to be the most common misperceptions about history? etc.

Also, a history of this sub-reddit might be interesting. How have the questions and answers changed over time? Has the provision of the FAQ altered the questions at all? How has the readership waxed and waned? What has been the impact of granting flairs? etc? etc?

I love u/elm11's title suggestion, '/r/Askhistorians Essays: Crowdsourcing Academia in the Online World", but feel that an analysis of the crowdsourcing would be a better book than a collection of the crowdsourcing.